Cremona's table of elliptic curves

6630 = 2 · 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 13- 17+	Signs for the Atkin-Lehner involutions
Class	6630f	Isogeny class
Conductor	6630	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	53760	Modular degree for the optimal curve
Δ	59574528000000 = 214 · 34 · 56 · 132 · 17	Discriminant
Eigenvalues	2+ 3+ 5-  0  2 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-447687,-115480971]	[a1,a2,a3,a4,a6]
Generators	[-387:216:1]	Generators of the group modulo torsion
j	9923129938500427467001/59574528000000	j-invariant
L	2.81084396448	L(r)(E,1)/r!
Ω	0.18456781205554	Real period
R	1.2691107643922	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53040cv1 19890x1 33150bx1 86190bo1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630f1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	-	0	2	-	+	-4	2	0	-4	6	-8	4	-8	-2	0	0	-8	12	-16	10	0	-10	-16

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Quadratic twists for elliptic curve 6630f1

-4	-3	5	13	17
53040cv1	19890x1	33150bx1	86190bo1	112710ba1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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